Russia's security services have not fully shared information that U.S. officials need to protect American athletes in the upcoming Sochi Winter Olympics, some U.S. lawmakers said on Sunday.

While Moscow is sending troops to southern Russia, where the games open next month, the Russians are not telling U.S. intelligence enough about threats from terrorist groups operating in the region, House Intelligence Committee Chairman Mike Rogers said.

"We don't seem to be getting all of the information we need to protect our athletes in the games," Rogers, a Republican, told CNN's "State of the Union with Candy Crowley."

"They're not giving us the full story about what are the threat streams, who do we need to worry about, are those groups - the terrorist groups who have had some success - are they still plotting?" Rogers said.

Sochi lies on the western edge of the Caucasus mountains, and militants trying to carve out an Islamist state in the region have threatened to attack the Olympic Games.

Russian President Vladimir Putin, who has staked his political and personal prestige on the success of the Olympics, has ordered safety measures beefed up nationwide after 34 people were killed last month in bombings in Volgograd, another city in southern Russia. About 37,000 Russian personnel are providing security in the Sochi area.

Putin, in an interview with foreign journalists including ABC's George Stephanopoulos that was aired on Sunday, said host Russia would do "whatever it takes" to ensure the security of Olympic participants and guests.

U.S. House Homeland Security Committee Chairman Michael McCaul, currently in Moscow, told ABC's "This Week" that cooperation with the Russians on security "could be a lot better." He said he was concerned about evacuation and emergency response plans from Sochi if something did happen there.

McCaul, who is also a Republican, said he would be meeting this week with the Russian government's "command and control of operations" in Sochi to assess the situation.

"We have 15,000 Americans traveling to Sochi for the Olympics. And I want to do everything I can to make sure it's a safe and successful Olympics," McCaul said.

The State Department has warned Americans planning to attend the games to be vigilant about their security due to potential terrorist threats.

Michael Morell, former deputy CIA director, said that while there is a long history of cooperation between nations hosting an Olympics and the U.S. intelligence community, "We did not get that cooperation with the Russians" for the Sochi games.

"I think fundamentally they don't want to admit that they don't have complete control here and they might need some help," Morell said on CBS' "Face the Nation."

One U.S. senator said he did not think the games would be safe enough for him or his relatives to attend.

"I would not go. And I don't think I would send my family," Senator Angus King, an independent from Maine, told CNN.